Because he's not only an OBE. He was knighted later on. Getting a higher honour later for continuing to give more services to whatever it is you do is not unusual.
KBE and GBE are only knighthoods in the Order of the British Empire. There are many other orders of chivalry in which you can be a knight, such as KCB (Knight Commander of the Order of the Bath), KCMG (Knight Commander of the Order of St Michael and St George), KCVO (Knight Commander of the Royal Victorian Order), and the G (Knight Grand Cross) versions of those. But the most common is a simple Knight Bachelor, which comes with no letters at all, just "Sir". Jackie Stewart is one of those.
KBE and GBE are in fact quite rare and are usually given to people who cannot use "Sir" so they can still show they have the honour. This includes Church of England clergy, who traditionally do not use "Sir", and honorary knights - those who are not citizens of one of Her Majesty's realms. An honorary knighthood is quite frequently given to US Presidents, for example.
And then there is Terry Wogan... who was awarded an honorary knighthood for services to broadcasting. Despite living in the UK for many years, he had remained an Irish citizen. Soon after the award was announced, he decided to naturalise as British, which meant he could be Sir Terry. Funny, that...